Two combinatorial optimization algorithms, tabu search and simulated annealing, are presented for the minimum-weight design of geometrically non-linear steel plane frames. The design algorithms obtain minimum weight frames by selecting suitable sections from a standard set of steel sections such as American Institute of Steel Construction (AISC) wide-flange (W) shapes. Stress constraints of AISC Load and Resistance Factor Design (LRFD) specification, maximum and interstorey drift constraints and size constraints for columns were imposed on frames. The stress constraints of AISC Allowable Stress Design (ASD) were also mounted in the two algorithms. The comparisons between AISC-LRFD and AISC-ASD specifications were also made while tabu search and simulated annealing were used separately. The algorithms were applied to the optimum design of three frame structures. The designs obtained using tabu search were compared to those where simulated annealing was considered. The comparisons showed that the tabu search algorithm yielded better designs with AISC-LRFD code specification.